In this paper I construct lattice models with an underlying U_q osp(2,2) superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These trigonometric R-matrices depend on three continuous parameters, the spectral parameter, the deformation parameter q and the U(1) parameter, b, of the superalgebra. It must be emphasized that the parameter q is generic and the parameter b does not correspond to the 'nilpotency' parameter of gs. The rational limits are given; they also

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... d on the U(1) parameter and this dependence cannot be rescaled away. I give the Bethe ansatz solution of the lattice models built from some of these R-matrices, while for other matrices, due to the particular nature of the representation theory of osp(2,2), I conjecture the result. The parameter b appears as a continuous generalized spin. Finally I briefly discuss the problem of finding the ground state of these models.